Introduction

Global importance of dripping

One to two paragraphs total

Have been hypothesized in several locations, but they are difficult to detect and controversial

One paragraph?

And so far, the drips have only been considered in isolation

One paragraph

Goals

One paragraph

Mechanisms (physics) of foundering

Rayleigh-Taylor instability (RTI)

 
Several mechanisms for lithospheric foundering have been proposed in the literature. The most common is the Rayleigh-Taylor instability (RTI), also known as gravitational instability, convective instability, or dripping \citep*{Houseman_1981}. In general, the RTI occurs when a fluid of greater density overlies a fluid of lesser density in a force field such as gravity, and refers to the unstable position of the interface between these fluids \citep{Chandrasekhar1961a}. In earth science, the RTI has been most widely used to model mantle plumes, which occur at the core-mantle boundary and ascend through the mantle. In the case of lithospheric foundering, the RTI may occur in the lower crust or mantle lithosphere and descend through the asthenosphere. The density inversion could occur by thickening of the crust and mantle lithosphere, which would push cold, dense lithosphere into warm, less dense asthenosphere \citep*{Houseman_1981}. Eclogitization of the lower crust could accompany thickening, which would increase its density beyond that of peridotite \citep*{Kay_1993}. Dense material could also form in the roots of arc batholiths as garnet pyroxenite restites or cumulates, called arclogites \citep*{Anderson_2005}.
Dense material overlying lighter material is an unstable configuration, one that can be triggered to reorganize through RTI. One trigger is a perturbation of the interface between the two layers. In this case, linear stability analysis is a useful way to understand what happens. Linear stability analysis begins with a small sinusoidal perturbation of the fluid interface for a set of initial and boundary conditions and asks which wavelength of perturbation will grow fastest. The fastest growing wavelength in the initial stages of instability will come to dominate other wavelengths and will lead to the development of drips with a characteristic spacing. Linear instability analysis also gives a function for the growth rate of this wavelength, at least during the early stages of instability.